Christopher Chan 🔸 comments on An Overview of the AI Safety Funding Situation

[Christopher Chan 🔸]

Shouldn’t the EMA calculation for 3 years be:

EMA = Current_year*2/​(3+1) + Last_yearEMA*(1 − 2/​(3+1))

EMA = Current_year*0.5 + Last_yearEMA*0.5

And EMA calculation for 2 years be (your google sheet formula):

EMA = Current_year*2/​(2+1) + Last_yearEMA*(1 − 2/​(2+1))

EMA = Current_year*0.66 + Last_yearEMA*0.33

However, in the google formula you weighted the previous year by 0.66 and the current year by 0.33, meaning that you gave the most recent data less weightings and the EMA is actually 2 years instead of 3?

https://​​pandas.pydata.org/​​pandas-docs/​​stable/​​reference/​​api/​​pandas.DataFrame.ewm.html
https://​​www.investopedia.com/​​terms/​​e/​​ema.asp

A slight change to use a 3 year-smoothing of a 3 year EMA

EMA(3 years) = Fund(t)*0.571+EMA(t-1)*0.286 + EMA(t-2)*0.143

*0.571+0.286+0.143 = ~ 1

I.e. 3 years EMA should actually be:

2014	0	0
2015	1186000	782760
2016	6563985	3971904.795
2017	43222473	25927931.53
2018	4280392	10427474.64
2019	63826400	43134826.36
2020	19626363	25034342.48
2021	90760985	65152624.55
2022	118717429	90001213.56
2023	30873035	52685675.37

[Stephen McAleese]

Thanks for pointing this out. I didn’t know there was a way to calculate the exponentially moving average (EMA) using NumPy.

Previously I was using alpha = 0.33 for weighting the current value. When that value is plugged into the formula alpha = 2 /​ N + 1, it means I was averaging over the past 5 years.

I’ve now decided to average over the past 4 years so the new alpha value is 0.4.